estimation of uncertainty in predicting ground level concentrations from direct source releases in an urban area using

Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 169
Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD
model equations
Vamsidhar V Poosarala, Ashok Kumar and Akhil Kadiyala

X

Estimation of uncertainty in predicting
ground level concentrations from direct source
releases in an urban area using the USEPA’s
AERMOD model equations

Vamsidhar V Poosarala, Ashok Kumar and Akhil Kadiyala
Department of Civil Engineering, The University of Toledo, Toledo, OH 43606

Abstract
One of the important prerequisites for a model to be used in decision making is to perform
uncertainty and sensitivity analyses on the outputs of the model. This study presents a
comprehensive review of the uncertainty and sensitivity analyses associated with prediction
of ground level pollutant concentrations using the USEPA’s AERMOD equations for point
sources. This is done by first putting together an approximate set of equations that are used
in the AERMOD model for the stable boundary layer (SBL) and convective boundary layer
(CBL). Uncertainty and sensitivity analyses are then performed by incorporating the
equations in Crystal Ball
®
software.
Various parameters considered for these analyses include emission rate, stack exit velocity,
stack exit temperature, wind speed, lateral dispersion parameter, vertical dispersion
parameter, weighting coefficients for both updraft and downdraft, total horizontal

distribution function, cloud cover, ambient temperature, and surface roughness length. The
convective mixing height is also considered for the CBL cases because it was specified. The
corresponding probability distribution functions, depending on the measured or practical
values are assigned to perform uncertainty and sensitivity analyses in both CBL and SBL
cases.
The results for uncertainty in predicting ground level concentrations at different downwind
distances in CBL varied between 67% and 75%, while it ranged between 40% and 47% in
SBL. The sensitivity analysis showed that vertical dispersion parameter and total horizontal
distribution function have contributed to 82% and 15% variance in predicting concentrations
in CBL. In SBL, vertical dispersion parameter and total horizontal distribution function have
contributed about 10% and 75% to variance in predicting concentrations respectively. Wind
speed has a negative contribution to variance and the other parameters had a negligent or
zero contribution to variance. The study concludes that the calculations of vertical
dispersion parameter for the CBL case and of horizontal distribution function for the SBL
case should be improved to reduce the uncertainty in predicting ground level
concentrations.

8
www.intechopen.com
Air Quality170

1. Introduction
Development of a good model for decision making in any field of study needs to be
associated with uncertainty and sensitivity analyses. Performing uncertainty and sensitivity
analyses on the output of a model is one of the basic prerequisites for model validation.
Uncertainty can be defined as a measure of the ‘goodness’ of a result. One can perform
uncertainty analysis to quantify the uncertainty associated with response of uncertainties in
model input. Sensitivity analysis helps determine the variation in model output due to
change in one or more input parameters for the model. Sensitivity analysis enables the
modeler to rank the input parameters by their contribution to variance of the output and

allows the modeler to determine the level of accuracy required for an input parameter to
make the models sufficiently useful and valid. If one considers an input value to be varying
from a standard existing value, then the person will be in a position to say by how much
more or less sensitivity will the output be on comparing with the case of a standard existing
value. By identifying the uncertainty and sensitivity of each model, a modeler gains the
capability of making better decisions when considering more than one model to obtain
desired accurate results. Hence, it is imperative for modelers to understand the importance
of recording and understanding the uncertainty and sensitivity of each model developed
that would assist industry and regulatory bodies in decision-making.
A review of literature on the application of uncertainty and sensitivity analyses helped us
gather some basic information on the applications of different methods in environmental
area and their performance in computing uncertainty and sensitivity. The paper focuses on
air quality modeling.
Various stages at which uncertainty can be obtained are listed below.
a) Estimation of uncertainties in the model inputs.
b) Estimation of the uncertainty in the results obtained from the model.
c) Characterizing the uncertainties by different model structure and model formulations.
d) Characterizing the uncertainties in model predicted results from the uncertainties in
evaluation data.
Hanna (1988) stated the total uncertainty involved in modeling simulations to be considered
as the sum of three components listed below.
a) Uncertainty due to errors in the model.
b) Uncertainty due to errors in the input data.
c) Uncertainty due to the stochastic processes in the atmosphere (like turbulence).
In order to estimate the uncertainty in predicting a variable using a model, the input
parameters to which the model is more sensitive should be determined. This is referred to as
sensitivity analysis, which indicates by how much the overall uncertainty in the model
predictions is associated with the individual uncertainty of the inputs in the model
[Vardoulakis et al. (2002)]. Sensitivity studies do not combine the uncertainty of the model
inputs, to provide a realistic estimate of uncertainty of model output or results. Sensitivity

analysis should be carried out for different variables of a model to decide where prominence
should be placed in estimating the total uncertainty. Sensitivity analysis of dispersion
parameters is useful, because, it promotes a deeper understanding of the phenomenon, and
helps one in placing enough emphasis in accurate measurements of the variables.

The analytical approach most frequently used for uncertainty analysis of simple equations is
variance propagation [IAEA (1989), Martz and Waller (1982), Morgan and Henrion (1990)].
To overcome problems encountered with analytical variance propagation equations,

numerical methods are useful in performing an uncertainty analysis. Various approaches for
determining uncertainty obtained from the literature include the following.
1) Differential uncertainty analysis [Cacuci (1981), and Worley (1987)] in which the partial
derivatives of the model response with respect to the parameters are used to estimate
uncertainty.
2) Monte Carlo analysis of statistical simplifications of complex models [Downing et al.
(1985), Mead and Pike (1975), Morton (1983), and Myers (1971), Kumar et al. (1999)].
3) Non-probabilistic methods [for example: fuzzy sets, fuzzy arithmetic, and possibility
theory [Ferson and Kuhn (1992)].
4) First-order analysis employing Taylor expansions [Scavia et al. (1981)].
5) Bootstrap method [Romano et al. (2004)].
6) Probability theory [Zadeh (1978)].
The most commonly applied numerical technique is the Monte Carlo simulation
(Rubinstein, 1981).
There are many methods by which sensitivity analysis can be performed. Some of the
methods are listed below.
1) Simple regression (on the untransformed and transformed data) [Brenkert et al. (1988)]
or visual analysis of output based on changes in input [(Kumar et al. (1987), Thomas
et al. (1985), Kumar et al. (2008)].
2) Multiple and piecewise multiple regression (on transformed and untransformed data)
[Downing et al. (1985)].

3) Regression coefficients and partial regression coefficients [Bartell et al. (1986), Gardner
et al. (1981)].
4) Stepwise regression and correlation ratios (on untransformed and transformed data).
5) Differential sensitivity analysis [Griewank and Corliss (1991), Worley (1987)].
6) Evidence theory [Dempster (1967), Shafer (1976)].
7) Interval approaches (Hansen and Walster, 2002).
8) ASTM method [(Kumar et al. (2002), Patel et al. (2003)].
Other studies that discuss the use of statistical regressions of the randomly selected values
of uncertain parameters on the values produced for model predictions to determine the
importance of parameters contributing to the overall uncertainty in the model result include
IAEA (1989), Iman et al. (1981a, 1981b), Iman and Helton (1991), and Morgan and Henrion
(1990).
Romano et al. (2004) performed the uncertainty analysis using Monte Carlo, Bootstrap, and
fuzzy methods to determine the uncertainty associated with air emissions from two electric
power plants in Italy. Emissions monitored were sulfur dioxide (SO
2
), nitrogen oxides
(NO
X
), carbon monoxide (CO), and particulate matter (PM). Daily average emission data
from a coal plant having two boilers were collected in 1998, and hourly average emission
data from a fuel oil plant having four boilers were collected in 2000. The study compared the
uncertainty analysis results from the three methods and concluded that Monte Carlo
method gave more accurate results when applied to the Gaussian distributions, while
Bootstrap method produced better results in estimating uncertainty for irregular and
asymmetrical distributions, and Fuzzy models are well suited for cases where there is
limited data availability or the data are not known properly.
Int Panis et al. (2004) studied the parametric uncertainty of aggregating marginal external
costs for all motorized road transportation modes to the national level air pollution in
www.intechopen.com

Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 171

1. Introduction
Development of a good model for decision making in any field of study needs to be
associated with uncertainty and sensitivity analyses. Performing uncertainty and sensitivity
analyses on the output of a model is one of the basic prerequisites for model validation.
Uncertainty can be defined as a measure of the ‘goodness’ of a result. One can perform
uncertainty analysis to quantify the uncertainty associated with response of uncertainties in
model input. Sensitivity analysis helps determine the variation in model output due to
change in one or more input parameters for the model. Sensitivity analysis enables the
modeler to rank the input parameters by their contribution to variance of the output and
allows the modeler to determine the level of accuracy required for an input parameter to
make the models sufficiently useful and valid. If one considers an input value to be varying
from a standard existing value, then the person will be in a position to say by how much
more or less sensitivity will the output be on comparing with the case of a standard existing
value. By identifying the uncertainty and sensitivity of each model, a modeler gains the
capability of making better decisions when considering more than one model to obtain
desired accurate results. Hence, it is imperative for modelers to understand the importance
of recording and understanding the uncertainty and sensitivity of each model developed
that would assist industry and regulatory bodies in decision-making.
A review of literature on the application of uncertainty and sensitivity analyses helped us
gather some basic information on the applications of different methods in environmental
area and their performance in computing uncertainty and sensitivity. The paper focuses on
air quality modeling.
Various stages at which uncertainty can be obtained are listed below.
a) Estimation of uncertainties in the model inputs.
b) Estimation of the uncertainty in the results obtained from the model.
c) Characterizing the uncertainties by different model structure and model formulations.
d) Characterizing the uncertainties in model predicted results from the uncertainties in

evaluation data.
Hanna (1988) stated the total uncertainty involved in modeling simulations to be considered
as the sum of three components listed below.
a) Uncertainty due to errors in the model.
b) Uncertainty due to errors in the input data.
c) Uncertainty due to the stochastic processes in the atmosphere (like turbulence).
In order to estimate the uncertainty in predicting a variable using a model, the input
parameters to which the model is more sensitive should be determined. This is referred to as
sensitivity analysis, which indicates by how much the overall uncertainty in the model
predictions is associated with the individual uncertainty of the inputs in the model
[Vardoulakis et al. (2002)]. Sensitivity studies do not combine the uncertainty of the model
inputs, to provide a realistic estimate of uncertainty of model output or results. Sensitivity
analysis should be carried out for different variables of a model to decide where prominence
should be placed in estimating the total uncertainty. Sensitivity analysis of dispersion
parameters is useful, because, it promotes a deeper understanding of the phenomenon, and
helps one in placing enough emphasis in accurate measurements of the variables.

The analytical approach most frequently used for uncertainty analysis of simple equations is
variance propagation [IAEA (1989), Martz and Waller (1982), Morgan and Henrion (1990)].
To overcome problems encountered with analytical variance propagation equations,

numerical methods are useful in performing an uncertainty analysis. Various approaches for
determining uncertainty obtained from the literature include the following.
1) Differential uncertainty analysis [Cacuci (1981), and Worley (1987)] in which the partial
derivatives of the model response with respect to the parameters are used to estimate
uncertainty.
2) Monte Carlo analysis of statistical simplifications of complex models [Downing et al.
(1985), Mead and Pike (1975), Morton (1983), and Myers (1971), Kumar et al. (1999)].
3) Non-probabilistic methods [for example: fuzzy sets, fuzzy arithmetic, and possibility
theory [Ferson and Kuhn (1992)].

4) First-order analysis employing Taylor expansions [Scavia et al. (1981)].
5) Bootstrap method [Romano et al. (2004)].
6) Probability theory [Zadeh (1978)].
The most commonly applied numerical technique is the Monte Carlo simulation
(Rubinstein, 1981).
There are many methods by which sensitivity analysis can be performed. Some of the
methods are listed below.
1) Simple regression (on the untransformed and transformed data) [Brenkert et al. (1988)]
or visual analysis of output based on changes in input [(Kumar et al. (1987), Thomas
et al. (1985), Kumar et al. (2008)].
2) Multiple and piecewise multiple regression (on transformed and untransformed data)
[Downing et al. (1985)].
3) Regression coefficients and partial regression coefficients [Bartell et al. (1986), Gardner
et al. (1981)].
4) Stepwise regression and correlation ratios (on untransformed and transformed data).
5) Differential sensitivity analysis [Griewank and Corliss (1991), Worley (1987)].
6) Evidence theory [Dempster (1967), Shafer (1976)].
7) Interval approaches (Hansen and Walster, 2002).
8) ASTM method [(Kumar et al. (2002), Patel et al. (2003)].
Other studies that discuss the use of statistical regressions of the randomly selected values
of uncertain parameters on the values produced for model predictions to determine the
importance of parameters contributing to the overall uncertainty in the model result include
IAEA (1989), Iman et al. (1981a, 1981b), Iman and Helton (1991), and Morgan and Henrion
(1990).
Romano et al. (2004) performed the uncertainty analysis using Monte Carlo, Bootstrap, and
fuzzy methods to determine the uncertainty associated with air emissions from two electric
power plants in Italy. Emissions monitored were sulfur dioxide (SO
2
), nitrogen oxides
(NO

X
), carbon monoxide (CO), and particulate matter (PM). Daily average emission data
from a coal plant having two boilers were collected in 1998, and hourly average emission
data from a fuel oil plant having four boilers were collected in 2000. The study compared the
uncertainty analysis results from the three methods and concluded that Monte Carlo
method gave more accurate results when applied to the Gaussian distributions, while
Bootstrap method produced better results in estimating uncertainty for irregular and
asymmetrical distributions, and Fuzzy models are well suited for cases where there is
limited data availability or the data are not known properly.
Int Panis et al. (2004) studied the parametric uncertainty of aggregating marginal external
costs for all motorized road transportation modes to the national level air pollution in
www.intechopen.com
Air Quality172

Belgium using the Monte Carlo technique. This study uses the impact pathway
methodology that involves basically following a pollutant from its emission until it causes
an impact or damage. The methodology involves details on the generation of emissions,
atmospheric dispersion, exposure of humans and environment to pollutants, and impacts on
public health, agriculture, and buildings. The study framework involves a combination of
emission models, and air dispersion models at local and regional scales with dose-response
functions and valuation rules. The propagation of errors was studied through complex
calculations and the error estimates of every parameter used for the calculation were
replaced by probability distribution. The above procedure is repeated many times (between
1000 and 10,000 trails) so that a large number of combinations of different input parameters
occur. For this analysis, all the calculations were performed using the Crystal Ball
®
software.
Based on the sensitivity of the result, parameters that contributed more to the variations
were determined and studied in detail to obtain a better estimate of the parameter. The
study observed the fraction high-emitter diesel passenger cars, air conditioning, and the

impacts of foreign trucks as the main factors contributing to uncertainty for 2010 estimate.
Sax and Isakov (2003) have estimated the contribution of variability and uncertainty in the
Gaussian air pollutant dispersion modeling systems from four model components:
emissions, spatial and temporal allocation of emissions, model parameters, and meteorology
using Monte Carlo simulations across ISCST3 and AERMOD. Variability and uncertainty in
predicted hexavalent chromium concentrations generated from welding operations were
studied. Results showed that a 95 percent confidence interval of predicted pollutant
concentrations varied in magnitude at each receptor indicating that uncertainty played an
important role at the receptors. AERMOD predicted a greater range of pollutant
concentration as compared to ISCST3 for low-level sources in this study. The conclusion of
the study was that input parameters need to be well characterized to reduce the uncertainty.
Rodriguez et al. (2007) investigated the uncertainty and sensitivity of ozone and PM
2.5

aerosols to variations in selected input parameters using a Monte Carlo analysis. The input
parameters were selected based on their potential in affecting the pollutant concentrations
predicted by the model and changes in emissions due to distributed generation (DG)
implementation in the South Coast Air Basin (SoCAB) of California. Numerical simulations
were performed using CIT three-dimensional air quality model. The magnitudes of the
largest impacts estimated in this study are greater and well beyond the contribution of
emissions uncertainty to the estimated air quality model error. Emissions introduced by DG
implementation produce a highly non-linear response in time and space on pollutant
concentrations. Results also showed that concentrating DG emissions in space or time
produced the largest air quality impacts in the SoCAB area. Thus, in addition to the total
amount of possible distributed generation to be installed, regulators should also consider
the type of DG installed (as well as their spatial distribution) to avoid undesirable air quality
impacts. After performing the sensitivity analysis, it was observed from the study that the
current model is good enough to predict the air quality impacts of DG emissions as long as
the changes in ozone are greater than 5 ppb and changes in PM
2.5

are greater than 13µg/m
3
.
Hwang et al. (1998) analyzed and discussed the techniques for model sensitivity and
uncertainty analyses, and analysis of the propagation of model uncertainty for the model
used within the GIS environment. A two-dimensional air quality model based on the first
order Taylor method was used in this study. The study observed brute force method, the
most straightforward method for sensitivity to be providing approximate solutions with

substantial human efforts. On the other hand, automatic differentiation required only one
model run with minimum human effort to compute the solution where results are accurate
to the precision of the machine. The study also observed that sampling methods provide
only partial information with unknown accuracy while first-order method combined with
automatic differentiation provide a complete solution with known accuracy. These
techniques can be used for any model that is first order differentiable.
Rao (2005) has discussed various types of uncertainties in the atmospheric dispersion
models and reviewed sensitivity and uncertainty analysis methods to characterize and/or
reduce them. This study concluded the results based on the confidence intervals (CI). If 5%
of CI for pollutant concentration is less than that of the regulatory standards, then remedial
measures must be taken. If the CI is more than 95% of the regulatory standards, nothing
needs to be done. If the 95% upper CI is above the standard and the 50
th
percentile is below,
further study must be carried out on the important parameters which play a key role in
calculation of the concentration value. If the 50
th
percentile is also above the standard, one
can proceed with cost effective remedial measures for risk reduction even though more
study needs to be carried out. The study concluded that the uncertainty analysis
incorporated into the atmospheric dispersion models would be valuable in decision-making.

Yegnan et al. (2002) demonstrated the need of incorporating uncertainty in dispersion
models by applying uncertainty to two critical input parameters (wind speed and ambient
temperature) in calculating the ground level concentrations. In this study, the Industrial
Source Complex Short Term (ISCST) model, which is a Gaussian dispersion model, is used
to predict the pollutant transport from a point source and the first-order and second-order
Taylor series are used to calculate the ground level uncertainties. The results of ISCST model
and uncertainty calculations are then validated with Monte Carlo simulations. There was a
linear relationship between inputs and output. From the results, it was observed that the
first-order Taylor series have been appropriate for ambient temperature and the second-
order series is appropriate for wind speed when compared to Monte Carlo method.
Gottschalk et al. (2007) tested the uncertainty associated with simulation of NEE (net
ecosystem exchange) by the PaSim (pasture simulation model) at four grassland sites. Monte
Carlo runs were performed for the years 2002 and 2003, using Latin Hypercube sampling
from probability density functions (PDF) for each input factor to know the effect of
measurement uncertainties in the main input factors like climate, atmospheric CO
2

concentrations, soil characteristics, and management. This shows that output uncertainty
not only depends on the input uncertainty, but also depends on the important factors and
the uncertainty in model simulations. The study concluded that if a system is more
environmentally confined, there will be higher uncertainties in the model results.
In addition to the above mentioned studies, many studies have focused on assessing the
uncertainty in air quality models [Freeman et al. (1986), Seigneur et al. (1992), Hanna et al.
(1998, 2001), Bergin et al. (1999), Yang et al. (1997), Moore and Londergan (2001), Hanna and
Davis (2002), Vardoulakis et al. (2002), Hakami et al. (2003), Jaarsveld et al. (1997), Smith et
al. (2000), and Guensler and Leonard (1995)]. Derwent and Hov (1988), Gao et al. (1996),
Phenix et al. (1998), Bergin et al. (1999), Grenfell et al. (1999), Hanna et al. (2001), and
Vuilleumier et al. (2001) have used the Monte Carlo simulations to address uncertainty in
regional-scale gas-phase mechanisms. Uncertainty in meteorology inputs was studied by
Irwin et al. (1987), and Dabberdt and Miller (2000), while the uncertainty in emissions was

observed by Frey and Rhodes (1996), Frey and Li (2002), and Frey and Zheng (2002).
www.intechopen.com
Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 173

Belgium using the Monte Carlo technique. This study uses the impact pathway
methodology that involves basically following a pollutant from its emission until it causes
an impact or damage. The methodology involves details on the generation of emissions,
atmospheric dispersion, exposure of humans and environment to pollutants, and impacts on
public health, agriculture, and buildings. The study framework involves a combination of
emission models, and air dispersion models at local and regional scales with dose-response
functions and valuation rules. The propagation of errors was studied through complex
calculations and the error estimates of every parameter used for the calculation were
replaced by probability distribution. The above procedure is repeated many times (between
1000 and 10,000 trails) so that a large number of combinations of different input parameters
occur. For this analysis, all the calculations were performed using the Crystal Ball
®
software.
Based on the sensitivity of the result, parameters that contributed more to the variations
were determined and studied in detail to obtain a better estimate of the parameter. The
study observed the fraction high-emitter diesel passenger cars, air conditioning, and the
impacts of foreign trucks as the main factors contributing to uncertainty for 2010 estimate.
Sax and Isakov (2003) have estimated the contribution of variability and uncertainty in the
Gaussian air pollutant dispersion modeling systems from four model components:
emissions, spatial and temporal allocation of emissions, model parameters, and meteorology
using Monte Carlo simulations across ISCST3 and AERMOD. Variability and uncertainty in
predicted hexavalent chromium concentrations generated from welding operations were
studied. Results showed that a 95 percent confidence interval of predicted pollutant
concentrations varied in magnitude at each receptor indicating that uncertainty played an
important role at the receptors. AERMOD predicted a greater range of pollutant

concentration as compared to ISCST3 for low-level sources in this study. The conclusion of
the study was that input parameters need to be well characterized to reduce the uncertainty.
Rodriguez et al. (2007) investigated the uncertainty and sensitivity of ozone and PM
2.5

aerosols to variations in selected input parameters using a Monte Carlo analysis. The input
parameters were selected based on their potential in affecting the pollutant concentrations
predicted by the model and changes in emissions due to distributed generation (DG)
implementation in the South Coast Air Basin (SoCAB) of California. Numerical simulations
were performed using CIT three-dimensional air quality model. The magnitudes of the
largest impacts estimated in this study are greater and well beyond the contribution of
emissions uncertainty to the estimated air quality model error. Emissions introduced by DG
implementation produce a highly non-linear response in time and space on pollutant
concentrations. Results also showed that concentrating DG emissions in space or time
produced the largest air quality impacts in the SoCAB area. Thus, in addition to the total
amount of possible distributed generation to be installed, regulators should also consider
the type of DG installed (as well as their spatial distribution) to avoid undesirable air quality
impacts. After performing the sensitivity analysis, it was observed from the study that the
current model is good enough to predict the air quality impacts of DG emissions as long as
the changes in ozone are greater than 5 ppb and changes in PM
2.5
are greater than 13µg/m
3
.
Hwang et al. (1998) analyzed and discussed the techniques for model sensitivity and
uncertainty analyses, and analysis of the propagation of model uncertainty for the model
used within the GIS environment. A two-dimensional air quality model based on the first
order Taylor method was used in this study. The study observed brute force method, the
most straightforward method for sensitivity to be providing approximate solutions with

substantial human efforts. On the other hand, automatic differentiation required only one
model run with minimum human effort to compute the solution where results are accurate
to the precision of the machine. The study also observed that sampling methods provide
only partial information with unknown accuracy while first-order method combined with
automatic differentiation provide a complete solution with known accuracy. These
techniques can be used for any model that is first order differentiable.
Rao (2005) has discussed various types of uncertainties in the atmospheric dispersion
models and reviewed sensitivity and uncertainty analysis methods to characterize and/or
reduce them. This study concluded the results based on the confidence intervals (CI). If 5%
of CI for pollutant concentration is less than that of the regulatory standards, then remedial
measures must be taken. If the CI is more than 95% of the regulatory standards, nothing
needs to be done. If the 95% upper CI is above the standard and the 50
th
percentile is below,
further study must be carried out on the important parameters which play a key role in
calculation of the concentration value. If the 50
th
percentile is also above the standard, one
can proceed with cost effective remedial measures for risk reduction even though more
study needs to be carried out. The study concluded that the uncertainty analysis
incorporated into the atmospheric dispersion models would be valuable in decision-making.
Yegnan et al. (2002) demonstrated the need of incorporating uncertainty in dispersion
models by applying uncertainty to two critical input parameters (wind speed and ambient
temperature) in calculating the ground level concentrations. In this study, the Industrial
Source Complex Short Term (ISCST) model, which is a Gaussian dispersion model, is used
to predict the pollutant transport from a point source and the first-order and second-order
Taylor series are used to calculate the ground level uncertainties. The results of ISCST model
and uncertainty calculations are then validated with Monte Carlo simulations. There was a
linear relationship between inputs and output. From the results, it was observed that the
first-order Taylor series have been appropriate for ambient temperature and the second-

order series is appropriate for wind speed when compared to Monte Carlo method.
Gottschalk et al. (2007) tested the uncertainty associated with simulation of NEE (net
ecosystem exchange) by the PaSim (pasture simulation model) at four grassland sites. Monte
Carlo runs were performed for the years 2002 and 2003, using Latin Hypercube sampling
from probability density functions (PDF) for each input factor to know the effect of
measurement uncertainties in the main input factors like climate, atmospheric CO
2

concentrations, soil characteristics, and management. This shows that output uncertainty
not only depends on the input uncertainty, but also depends on the important factors and
the uncertainty in model simulations. The study concluded that if a system is more
environmentally confined, there will be higher uncertainties in the model results.
In addition to the above mentioned studies, many studies have focused on assessing the
uncertainty in air quality models [Freeman et al. (1986), Seigneur et al. (1992), Hanna et al.
(1998, 2001), Bergin et al. (1999), Yang et al. (1997), Moore and Londergan (2001), Hanna and
Davis (2002), Vardoulakis et al. (2002), Hakami et al. (2003), Jaarsveld et al. (1997), Smith et
al. (2000), and Guensler and Leonard (1995)]. Derwent and Hov (1988), Gao et al. (1996),
Phenix et al. (1998), Bergin et al. (1999), Grenfell et al. (1999), Hanna et al. (2001), and
Vuilleumier et al. (2001) have used the Monte Carlo simulations to address uncertainty in
regional-scale gas-phase mechanisms. Uncertainty in meteorology inputs was studied by
Irwin et al. (1987), and Dabberdt and Miller (2000), while the uncertainty in emissions was
observed by Frey and Rhodes (1996), Frey and Li (2002), and Frey and Zheng (2002).
www.intechopen.com
Air Quality174

Seigneur et al. (1992), Frey (1993), and Cullen and Frey (1999) have assessed the uncertainty
for a health risk assessment.
From the literature review, it was observed that uncertainty and sensitivity analyses have
been carried out for various cases having different model parameters for varying emissions
inventories, air pollutants, air quality modeling, and dispersion models. However, only one

of these studies [Sax and Isakov (2003)] reported in the literature discussed such application
of uncertainty and sensitivity analyses for predicting ground level concentrations using
AERMOD equations. This study tries to fill this knowledge gap by performing uncertainty
and sensitivity analyses of the results obtained at ground level from the AERMOD
equations using urban area emission data with Crystal Ball
®
software.

2. Methodology
This section provides a detailed overview of the various steps adopted by the researchers
when performing uncertainty and sensitivity analyses over predicted ground level pollutant
concentrations from a point source in an urban area using the United States Environmental
Protection Agency’s (U.S. EPA’s) AERMOD equations. The study focuses on determining
the uncertainty in predicting ground level pollutant concentrations using the AERMOD
equations.

2.1 AERMOD Spreadsheet Development
The researchers put together an approximate set of equations that are used in the AERMOD
model for the stable boundary layer (SBL) and convective boundary layer (CBL). Note that
the AERMOD model treats atmospheric conditions either as stable or convective. The basic
equations used for calculating concentrations in both CBL and SBL are programmed in a
spreadsheet. The following is a list of assumptions used while deriving the parameters and
choosing the concentration equations in both SBL and CBL.
1) Only direct source equation is taken to calculate the pollutant concentration in CBL.
However, there is only one equation for all conditions in the stable boundary layer.
2) The fraction of plume mass concentration in CBL is taken as one. This assumes that
the plume will not penetrate the convective boundary layer at any point during
dispersion and plume is dispersing within the CBL.
3) The value of convective mixing height is taken by assuming a value for each hour i.e.,
it is not computed using the equations given in the AERMOD manual.

2.1.1 Stable Boundary Layer (SBL) and Convective Boundary Layer (CBL) Equations
This section presents the AERMOD model equations that are incorporated in to the
AERMOD spreadsheet for stable and convective boundary layer conditions.

2.1.1a Concentration Calculations in the SBL and CBL*
For stable boundary conditions, the AERMOD concentration expression (C
s
in equation 1a)
has the Gaussian form, and is similar to that used in many other steady-state plume models.
The equation for Cs is given by,


(1a)
For the case of m = 1 (i.e. m= -1, 0, 1), the above equation changes to the form of equation 1b.

(1b)
The equation for calculation of the pollutant concentration in the convective boundary layer
is given by equation 2a.

(2a)
for m = 1 (i.e. m= 0, 1) the above equations changes to the form of equation 2b.


(2b)
* The symbols are explained in the Nomenclature section at the end of the Chapter.

2.1.1b Friction Velocity (u
*
) in SBL and CBL

The computation of friction velocity (u
*
) under SBL conditions is given by equation 3.

(3)

where, [Hanna and Chang (1993), Perry (1992)] (4)

[Garratt (1992)] (5)


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Estimation of uncertainty in predicting ground level concentrations from
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Seigneur et al. (1992), Frey (1993), and Cullen and Frey (1999) have assessed the uncertainty
for a health risk assessment.
From the literature review, it was observed that uncertainty and sensitivity analyses have
been carried out for various cases having different model parameters for varying emissions
inventories, air pollutants, air quality modeling, and dispersion models. However, only one
of these studies [Sax and Isakov (2003)] reported in the literature discussed such application
of uncertainty and sensitivity analyses for predicting ground level concentrations using
AERMOD equations. This study tries to fill this knowledge gap by performing uncertainty
and sensitivity analyses of the results obtained at ground level from the AERMOD
equations using urban area emission data with Crystal Ball
®
software.

2. Methodology
This section provides a detailed overview of the various steps adopted by the researchers

when performing uncertainty and sensitivity analyses over predicted ground level pollutant
concentrations from a point source in an urban area using the United States Environmental
Protection Agency’s (U.S. EPA’s) AERMOD equations. The study focuses on determining
the uncertainty in predicting ground level pollutant concentrations using the AERMOD
equations.

2.1 AERMOD Spreadsheet Development
The researchers put together an approximate set of equations that are used in the AERMOD
model for the stable boundary layer (SBL) and convective boundary layer (CBL). Note that
the AERMOD model treats atmospheric conditions either as stable or convective. The basic
equations used for calculating concentrations in both CBL and SBL are programmed in a
spreadsheet. The following is a list of assumptions used while deriving the parameters and
choosing the concentration equations in both SBL and CBL.
1) Only direct source equation is taken to calculate the pollutant concentration in CBL.
However, there is only one equation for all conditions in the stable boundary layer.
2) The fraction of plume mass concentration in CBL is taken as one. This assumes that
the plume will not penetrate the convective boundary layer at any point during
dispersion and plume is dispersing within the CBL.
3) The value of convective mixing height is taken by assuming a value for each hour i.e.,
it is not computed using the equations given in the AERMOD manual.

2.1.1 Stable Boundary Layer (SBL) and Convective Boundary Layer (CBL) Equations
This section presents the AERMOD model equations that are incorporated in to the
AERMOD spreadsheet for stable and convective boundary layer conditions.

2.1.1a Concentration Calculations in the SBL and CBL*
For stable boundary conditions, the AERMOD concentration expression (C
s
in equation 1a)
has the Gaussian form, and is similar to that used in many other steady-state plume models.

The equation for Cs is given by,


(1a)
For the case of m = 1 (i.e. m= -1, 0, 1), the above equation changes to the form of equation 1b.

(1b)
The equation for calculation of the pollutant concentration in the convective boundary layer
is given by equation 2a.

(2a)
for m = 1 (i.e. m= 0, 1) the above equations changes to the form of equation 2b.


(2b)
* The symbols are explained in the Nomenclature section at the end of the Chapter.

2.1.1b Friction Velocity (u
*
) in SBL and CBL
The computation of friction velocity (u
*
) under SBL conditions is given by equation 3.

(3)

where, [Hanna and Chang (1993), Perry (1992)] (4)

[Garratt (1992)] (5)

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Air Quality176

Substituting equations 4 and 5 in equation 3, one gets the equation of friction velocity, u
*
for
SBL conditions, as given by equation 6.


(6)
The computation of friction velocity u
*
under CBL conditions is given by equation 7.


(7)

2.1.1c Effective Stack Height in SBL
The effective stack height (h
es
) is given by equation 8.


(8)

where, Δh
s
is calculated by using equation 9.

(9)

where, N’=0.7N,


(10)
(K m
-1
) is potential temperature gradient.


(11)


(12)

2.1.1d Height of the Reflecting Surface in SBL
The height of reflecting surface in stable boundary layer is computed using equation 13.


(13)

where,

(14)

(15)

(16)
[Venkatram et.al., 1984]
(17)

l
n
= 0.36.h
es
and l
s
= 0.27. ( ), z
i
= z
im
.


2.1.1e Total Height of the Direct Source Plume in CBL
The actual height of the direct source plume will be the combination of the release height,
buoyancy, and convection. The equation for total height of the direct source plume is given
by equation 18.

(18)

(19)

w
j
= a
j

.w
*
where, subscript j is equal to 1 for updrafts and 2 for the downdrafts.
λ
j
in equation 2 is given by λ
1
and λ
2
for updraft and downdraft respectively and they are
calculated using equations 20 and 21 respectively.


(20)


(21)

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Estimation of uncertainty in predicting ground level concentrations from
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Substituting equations 4 and 5 in equation 3, one gets the equation of friction velocity, u
*
for
SBL conditions, as given by equation 6.


(6)
The computation of friction velocity u

*
under CBL conditions is given by equation 7.


(7)

2.1.1c Effective Stack Height in SBL
The effective stack height (h
es
) is given by equation 8.


(8)

where, Δh
s
is calculated by using equation 9.


(9)

where, N’=0.7N,


(10)
(K m
-1
) is potential temperature gradient.

(11)


(12)

2.1.1d Height of the Reflecting Surface in SBL
The height of reflecting surface in stable boundary layer is computed using equation 13.


(13)

where,

(14)

(15)


(16)
[Venkatram et.al., 1984]

(17)

l
n
= 0.36.h
es
and l
s
= 0.27. ( ), z

i
= z
im
.


2.1.1e Total Height of the Direct Source Plume in CBL
The actual height of the direct source plume will be the combination of the release height,
buoyancy, and convection. The equation for total height of the direct source plume is given
by equation 18.

(18)

(19)

w
j
= a
j
.w
*
where, subscript j is equal to 1 for updrafts and 2 for the downdrafts.
λ
j
in equation 2 is given by λ
1
and λ
2
for updraft and downdraft respectively and they are
calculated using equations 20 and 21 respectively.

(20)


(21)

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Air Quality178


(22)

(23)

and β
2
=1+R
2

R is assumed to be 2 [Weil et al. 1997],
where, the fraction of is decided with the condition given below.
= 0.125; for H
p
≥ 0.1z
i
and = 1.25. for H
p
< 0.1z
i

z
i
= MAX [z
ic
, z
im
].

2.1.1f Monin-Obukhov length (L) and Sensible heat flux (H) for SBL and CBL
Monin-Obukhov length (L) and Sensible heat flux (H) are calculated using equations 24 and
25 respectively.

(24)

(25)

Product of u
*
and θ
*
can be taken as 0.05 m s
-1
K [Hanna et al. (1986)].

2.1.1g Convective velocity scale (w
*
) for SBL and CBL
The equation for convective velocity (w
*

) is computed using equation 26.

(26)

2.1.1h Lateral distribution function (F
y
)
This function is calculated because the chances of encountering the coherent plume after
travelling some distance will be less. Taking the above into consideration, the lateral
distribution function is calculated. This equation will be in a Gaussian form.


(27)


σ
y
, the lateral dispersion parameter is calculated using equation 28 as given by Kuruvilla
et.al. (2005).

(28)

which is the lateral turbulence.

2.1.1i Vertical dispersion parameter (σ
z
) for SBL and CBL
The equation for vertical dispersion parameter is given by equation 29.

(29)


(30)
Table 1 presents the list of parameters used by AERMOD spreadsheet in predicting pollutant
concentrations and Table 2 presents the basic inputs required to calculate the parameters.

Table 1. Different Parameters Used for Predicting Pollutant Concentration in AERMOD
Spreadsheet.

Source Data
Meteorological
Data
Surface Parameters
Other Data and
Constants
Height of stack
(h
s
)
Ambient
temperature (T
a
)
Monin-Obukhov
length (L)
Downwind
distance (x)
Radius of stack
(r

s
)
Cloud cover (n) Surface heat flux (H)
Acceleration due to
gravity (g)
Stack exit gas
temperature (T
s
)
Surface roughness
length (z
o
)
Mechanical mixing
height (z
im
)
Specific heat (c
p
)
Emission rate (Q)

Convective mixing
height (z
ic
)
Density of air (ρ)
Stack exit gas
velocity (w
s

)
Wind speed (u) Time (t)

Brunt-Vaisala
frequency (N)
Van Karman
constant (k = 0.4)
Temperature scale (θ
*
)
multiple reflections
(m)
Vertical turbulence
(σ
wt
)
β
m
= 5

β
t
= 2
β = 0.6
R = 2
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Estimation of uncertainty in predicting ground level concentrations from
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(22)

(23)

and β
2
=1+R
2

R is assumed to be 2 [Weil et al. 1997],
where, the fraction of is decided with the condition given below.
= 0.125; for H
p
≥ 0.1z
i
and = 1.25. for H
p
< 0.1z
i

z
i
= MAX [z
ic
, z
im
].

2.1.1f Monin-Obukhov length (L) and Sensible heat flux (H) for SBL and CBL
Monin-Obukhov length (L) and Sensible heat flux (H) are calculated using equations 24 and

25 respectively.

(24)

(25)

Product of u
*
and θ
*
can be taken as 0.05 m s
-1
K [Hanna et al. (1986)].

2.1.1g Convective velocity scale (w
*
) for SBL and CBL
The equation for convective velocity (w
*
) is computed using equation 26.

(26)

2.1.1h Lateral distribution function (F
y
)
This function is calculated because the chances of encountering the coherent plume after
travelling some distance will be less. Taking the above into consideration, the lateral
distribution function is calculated. This equation will be in a Gaussian form.

(27)


σ
y
, the lateral dispersion parameter is calculated using equation 28 as given by Kuruvilla
et.al. (2005).

(28)

which is the lateral turbulence.

2.1.1i Vertical dispersion parameter (σ
z
) for SBL and CBL
The equation for vertical dispersion parameter is given by equation 29.


(29)


(30)
Table 1 presents the list of parameters used by AERMOD spreadsheet in predicting pollutant
concentrations and Table 2 presents the basic inputs required to calculate the parameters.

Table 1. Different Parameters Used for Predicting Pollutant Concentration in AERMOD
Spreadsheet.

Source Data

Meteorological
Data
Surface Parameters
Other Data and
Constants
Height of stack
(h
s
)
Ambient
temperature (T
a
)
Monin-Obukhov
length (L)
Downwind
distance (x)
Radius of stack
(r
s
)
Cloud cover (n) Surface heat flux (H)
Acceleration due to
gravity (g)
Stack exit gas
temperature (T
s
)
Surface roughness
length (z

o
)
Mechanical mixing
height (z
im
)
Specific heat (c
p
)
Emission rate (Q)

Convective mixing
height (z
ic
)
Density of air (ρ)
Stack exit gas
velocity (w
s
)
Wind speed (u) Time (t)

Brunt-Vaisala
frequency (N)
Van Karman
constant (k = 0.4)
Temperature scale (θ
*
)
multiple reflections

(m)
Vertical turbulence
(σ
wt
)
β
m
= 5

β
t
= 2
β = 0.6
R = 2
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Air Quality180

Parameters Basic Inputs
Plume buoyancy flux (F
b
)
T
a
, T
s
, W
s
, r
s
Plume momentum flux (F

m
) T
a
, T
s
, W
s
, r
s
Surface friction velocity (u
*
) u, z
ref
, z
o
Sensible heat flux (H)
u, z
ref
, z
o
, n
Convective velocity scale (w
*
) u, z
ref
, z
o
, n, z
ic
, T

ref
Monin-Obukhov length (L)
u, z
ref
, z
o
, n, T
ref
,
Temperature scale (θ
*
)
N
Lateral turbulence (σ
v
)
u, z
ref
, z
o
, n, z
ic
, T
ref
Total vertical turbulence (σ
wt
) u, z
ref
, z
o

, n, z
ic
, T
ref
, z
i
Length scale (l)
u, z
ref
, z
o
, n, z
ic
, T
ref
, z
i
, T
a
, T
s
, W
s
, h
s
, r
s
Brunt-Vaisala frequency (N)
T
a

Mechanical mixing height
u, z
ref
, z
o
, t
Convective mixing height
u, z
ref
, z
o
, n, T
a
Potential temperature
T
a
Table 2. Basic Inputs Required to Calculate the Parameters.

After programming all the above equations into EXCEL spreadsheet, they are then
incorporated into Crystal ball
®
software to perform uncertainty and sensitivity analyses.
Refer to Poosarala et al. (2009) for more information on the application and use of AERMOD
spreadsheet. The output from this spreadsheet was compared with the actual runs made
using the AERMOD model for a limited number of cases. The concentrations from both
AERMOD model and AERMOD equations are calculated using source data (refer to Tables
3, 4, and 5) and metrological data from scalar data for the three days (February 11, June 29,
October 22 of 1992) for Flint, Michigan. The predicted concentration values from the
AERMOD model are taken and divided into two groups as CBL and SBL based on the
Monin-Obukhov length (L) i.e. if L > 0 then it is SBL and vice versa. These results are then

compared with AERMOD spreadsheet predicted concentrations for each boundary layer
condition. For this comparison, three different cases considering varying emission velocities
and stack temperatures for 40 meter, 70 meter, and 100 meter stacks are used for analyzing
both the convective and stable atmospheric conditions.
The source data for the comparison of concentrations are taken in sets (represented by set
numbers – 1, 2, and 3). In the first set of source group (1-1, 1-2, 1-3 in Tables 3-5), height of
stack is kept constant, while exit velocity of the pollutant, stack temperature, and diameter
of the stack are changed as shown in Tables 3, 4, and 5. For sets two and three, stack
temperature and exit velocity are kept unchanged respectively. The study found results for
comparison of predicted concentrations from AERMOD spreadsheet to vary in the range of
87% - 107% when compared to predicted concentrations from AERMOD model. Hence, one
can say that the approximate sets of equations used in AERMOD spreadsheet were able to
reproduce the AERMOD results.


Sets
Height of
Stack (m)
Diameter of
Stack (m)
Stack Exit
Temperature (
o
K)
Stack Exit
Velocity (ms
-1
)
Emission
Rate (gs

-1
)
1-1 100 8 300 15 20
1-2 100 8 346 10 20
1-3 100 8 373 5 20
2-3 100 8 373 15 15
3-1 100 8 373 15 17.4
Table 3. Source Data for Evaluation of AERMODSBL and AERMODCBL Test Cases for 100
m Stack.


Sets
Height of
Stack (m)
Diameter of
Stack (m)
Stack Exit
Temperature (
o
K)
Stack Exit
Velocity (ms
-1
)
Emission
Rate (gs
-1
)
2-2 70 6 373 10 15
3-2 70 6 346 15 17.4

4-1 70 6 300 5 20
Table 4. Source Data for Evaluation of AERMODSBL and AERMODCBL Test Cases for 70 m
Stack


Sets
Height of
Stack (m)
Diameter of
Stack (m)
Stack Exit
Temperature (
o
K)
Stack Exit
Velocity (ms
-1
)
Emission
Rate (gs
-1
)
2-1 40 4 373 10 15
3-3 40 4 346 15 17.4
4-2 40 4 300 5 20
Table 5. Source Data for Evaluation of AERMODSBL and AERMODCBL Test Cases for 40 m
Stack

Next, the above sets of equations are incorporated in the Crystal Ball
®

software for
performing the uncertainty and sensitivity analyses. To perform these analyses in
calculating the predicted concentrations using AERMOD equations, first the forecasting cell
and assumption cells are to be defined. Pollutant concentration is designated to be the
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Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 181

Parameters Basic Inputs
Plume buoyancy flux (F
b
) T
a
, T
s
, W
s
, r
s
Plume momentum flux (F
m
) T
a
, T
s
, W
s
, r
s
Surface friction velocity (u

*
) u, z
ref
, z
o
Sensible heat flux (H)
u, z
ref
, z
o
, n
Convective velocity scale (w
*
) u, z
ref
, z
o
, n, z
ic
, T
ref
Monin-Obukhov length (L)
u, z
ref
, z
o
, n, T
ref
,
Temperature scale (θ

*
)
N
Lateral turbulence (σ
v
) u, z
ref
, z
o
, n, z
ic
, T
ref
Total vertical turbulence (σ
wt
) u, z
ref
, z
o
, n, z
ic
, T
ref
, z
i
Length scale (l)
u, z
ref
, z
o

, n, z
ic
, T
ref
, z
i
, T
a
, T
s
, W
s
, h
s
, r
s
Brunt-Vaisala frequency (N)
T
a
Mechanical mixing height
u, z
ref
, z
o
, t
Convective mixing height
u, z
ref
, z
o

, n, T
a
Potential temperature
T
a
Table 2. Basic Inputs Required to Calculate the Parameters.

After programming all the above equations into EXCEL spreadsheet, they are then
incorporated into Crystal ball
®
software to perform uncertainty and sensitivity analyses.
Refer to Poosarala et al. (2009) for more information on the application and use of AERMOD
spreadsheet. The output from this spreadsheet was compared with the actual runs made
using the AERMOD model for a limited number of cases. The concentrations from both
AERMOD model and AERMOD equations are calculated using source data (refer to Tables
3, 4, and 5) and metrological data from scalar data for the three days (February 11, June 29,
October 22 of 1992) for Flint, Michigan. The predicted concentration values from the
AERMOD model are taken and divided into two groups as CBL and SBL based on the
Monin-Obukhov length (L) i.e. if L > 0 then it is SBL and vice versa. These results are then
compared with AERMOD spreadsheet predicted concentrations for each boundary layer
condition. For this comparison, three different cases considering varying emission velocities
and stack temperatures for 40 meter, 70 meter, and 100 meter stacks are used for analyzing
both the convective and stable atmospheric conditions.
The source data for the comparison of concentrations are taken in sets (represented by set
numbers – 1, 2, and 3). In the first set of source group (1-1, 1-2, 1-3 in Tables 3-5), height of
stack is kept constant, while exit velocity of the pollutant, stack temperature, and diameter
of the stack are changed as shown in Tables 3, 4, and 5. For sets two and three, stack
temperature and exit velocity are kept unchanged respectively. The study found results for
comparison of predicted concentrations from AERMOD spreadsheet to vary in the range of
87% - 107% when compared to predicted concentrations from AERMOD model. Hence, one

can say that the approximate sets of equations used in AERMOD spreadsheet were able to
reproduce the AERMOD results.


Sets
Height of
Stack (m)
Diameter of
Stack (m)
Stack Exit
Temperature (
o
K)
Stack Exit
Velocity (ms
-1
)
Emission
Rate (gs
-1
)
1-1 100 8 300 15 20
1-2 100 8 346 10 20
1-3 100 8 373 5 20
2-3 100 8 373 15 15
3-1 100 8 373 15 17.4
Table 3. Source Data for Evaluation of AERMODSBL and AERMODCBL Test Cases for 100
m Stack.

Sets
Height of
Stack (m)
Diameter of
Stack (m)
Stack Exit
Temperature (
o
K)
Stack Exit
Velocity (ms
-1
)
Emission
Rate (gs
-1
)
2-2 70 6 373 10 15
3-2 70 6 346 15 17.4
4-1 70 6 300 5 20
Table 4. Source Data for Evaluation of AERMODSBL and AERMODCBL Test Cases for 70 m
Stack


Sets
Height of
Stack (m)
Diameter of
Stack (m)
Stack Exit

Temperature (
o
K)
Stack Exit
Velocity (ms
-1
)
Emission
Rate (gs
-1
)
2-1 40 4 373 10 15
3-3 40 4 346 15 17.4
4-2 40 4 300 5 20
Table 5. Source Data for Evaluation of AERMODSBL and AERMODCBL Test Cases for 40 m
Stack

Next, the above sets of equations are incorporated in the Crystal Ball
®
software for
performing the uncertainty and sensitivity analyses. To perform these analyses in
calculating the predicted concentrations using AERMOD equations, first the forecasting cell
and assumption cells are to be defined. Pollutant concentration is designated to be the
www.intechopen.com
Air Quality182

forecasting cell, and parameters such as emission rate, stack exit velocity, stack temperature,
wind speed, lateral dispersion parameter, vertical dispersion parameter, weighting coefficients
for both updraft and downdraft, total horizontal distribution function, cloud cover, ambient
temperature, and surface roughness length are defined as assumption cells. Their

corresponding probability distribution functions, depending on the measured or practical
values are assigned to get the uncertainty and sensitivity analyses of the forecasting cell in
both convective and stable conditions (refer to Table 6). In addition to the above input values,
convective mixing height is also taken as another assumption cell in CBL as the value of
convective mixing height is directly taken, rather than calculating it using its integral form of
equation. Convective mixing height governs the equation of total vertical turbulence, which is
used for calculating the vertical dispersion parameter. An accepted error of ±10% of the value
is applied for the parameters in both assumption and forecasting cells while performing
uncertainty and sensitivity analyses in predicting ground level concentrations.
For each set of data, the analyses are carried at different downwind distances. In the case of
height of stacks being constant, uncertainty and sensitivity analyses were performed at three
different downwind distances: distance near the maximum concentration value, next nearest
distance point to the stack coordinates, and a farthest point. For the other cases where the
range for parameters wind speed, Monin-Obukhov length, and ambient temperature are
considered, the hour with the lowest and highest value from range are taken (refer to Table
7) and the predicted concentrations from that hour are considered for uncertainty and
sensitivity analysis. These values are applicable for the days considered. For CBL condition,
separate case is considered by taking two values of surface roughness length (0.03 m for
urban area with isolated obstructions and 1 m for urban area with large buildings).


Parameter
Probability Distribution
Function

Reference
CBL SBL
Lateral distribution (σ
y
) Gaussian Gaussian

Willis and Deardorff
(1981), Briggs (1993)
Vertical distribution (σ
z
) bi-Gaussian Gaussian
Willis and Deardorff
(1981), Briggs (1993)
Wind velocity (u) Weibull Weibull Sathyajith (2002)
Total horizontal distribution
function (F
y
)
Gaussian Gaussian Lamb (1982)
Weighting coefficients for both
updraft and downdraft (λ
1
and λ
2
)
bi-Gaussian NA Weil et al. (1997)
Stack exit temperature (T) Gaussian Gaussian Gabriel (1994)
Stack exit velocity (W
s
) Gaussian Gaussian

Emission rate (Q)
Gaussian
Gaussian
Eugene et al. (2008)
Table 6. Assumption Cells and Their Assigned Probability Distribution Functions.

Parameter
SBL CBL
Lowest Highest Lowest Highest
Wind speed (ms
-1
) 1.5 9.3 3.6 8.2
Ambient temperature (
o
K) 262.5 294.9 267.5 302
Monin-Obukhov length (m) 38.4 8888 -8888 -356
Table 7. Summary of Parameters Considered for Uncertainty and Sensitivity Analyses.

3. Results and discussion
3.1 Uncertainty Analysis

3.1.1a 100 m Stack
The predicted concentrations from 100 m high stacks for the defined assumption cells have
shown an uncertainty range of 55 to 80% for an error of ± 10% (i.e., uncertainty of the
concentration equations to calculate ground level concentration within a range of 10% from
the predicted value) for all the parameters in convective boundary layer (CBL) for surface
roughness length (Z
o
) value of 0.03 meter. When Z
o
is 1 meter, the uncertainty ranged
between 72 and 74%. In the case of stable boundary layer, the uncertainty ranged from 40 to
45% for the defined assumption cells. Bhat (2008) performed uncertainty and sensitivity
analyses for two Gaussian models used by Bower et al. (1979) and Chen et al. (1998) for

modeling bioaerosol emissions from land applications of class B biosolids. He observed
uncertainty ranges of 54 to 63% and 55 to 60% for Bowers et al. (1979) and Chen et al. (1998)
models respectively, for a ground level source.
Figures 1 through 6 present the uncertainty charts for both convective and stable
atmospheric conditions at different downwind distances. It was observed that the
atmospheric stability conditions influenced the uncertainty value. The uncertainty value
decreased as the atmospheric stability condition changed from convective to stable.

www.intechopen.com
Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 183

forecasting cell, and parameters such as emission rate, stack exit velocity, stack temperature,
wind speed, lateral dispersion parameter, vertical dispersion parameter, weighting coefficients
for both updraft and downdraft, total horizontal distribution function, cloud cover, ambient
temperature, and surface roughness length are defined as assumption cells. Their
corresponding probability distribution functions, depending on the measured or practical
values are assigned to get the uncertainty and sensitivity analyses of the forecasting cell in
both convective and stable conditions (refer to Table 6). In addition to the above input values,
convective mixing height is also taken as another assumption cell in CBL as the value of
convective mixing height is directly taken, rather than calculating it using its integral form of
equation. Convective mixing height governs the equation of total vertical turbulence, which is
used for calculating the vertical dispersion parameter. An accepted error of ±10% of the value
is applied for the parameters in both assumption and forecasting cells while performing
uncertainty and sensitivity analyses in predicting ground level concentrations.
For each set of data, the analyses are carried at different downwind distances. In the case of
height of stacks being constant, uncertainty and sensitivity analyses were performed at three
different downwind distances: distance near the maximum concentration value, next nearest
distance point to the stack coordinates, and a farthest point. For the other cases where the
range for parameters wind speed, Monin-Obukhov length, and ambient temperature are

considered, the hour with the lowest and highest value from range are taken (refer to Table
7) and the predicted concentrations from that hour are considered for uncertainty and
sensitivity analysis. These values are applicable for the days considered. For CBL condition,
separate case is considered by taking two values of surface roughness length (0.03 m for
urban area with isolated obstructions and 1 m for urban area with large buildings).


Parameter
Probability Distribution
Function

Reference
CBL SBL
Lateral distribution (σ
y
) Gaussian Gaussian
Willis and Deardorff
(1981), Briggs (1993)
Vertical distribution (σ
z
) bi-Gaussian Gaussian
Willis and Deardorff
(1981), Briggs (1993)
Wind velocity (u) Weibull Weibull Sathyajith (2002)
Total horizontal distribution
function (F
y
)
Gaussian Gaussian Lamb (1982)
Weighting coefficients for both

updraft and downdraft (λ
1
and λ
2
)
bi-Gaussian NA Weil et al. (1997)
Stack exit temperature (T) Gaussian Gaussian Gabriel (1994)
Stack exit velocity (W
s
) Gaussian Gaussian

Emission rate (Q) Gaussian Gaussian Eugene et al. (2008)
Table 6. Assumption Cells and Their Assigned Probability Distribution Functions.


Parameter
SBL CBL
Lowest
Highest
Lowest
Highest
Wind speed (ms
-1
) 1.5 9.3 3.6 8.2
Ambient temperature (
o
K) 262.5 294.9 267.5 302
Monin-Obukhov length (m) 38.4 8888 -8888 -356
Table 7. Summary of Parameters Considered for Uncertainty and Sensitivity Analyses.

3. Results and discussion
3.1 Uncertainty Analysis

3.1.1a 100 m Stack
The predicted concentrations from 100 m high stacks for the defined assumption cells have
shown an uncertainty range of 55 to 80% for an error of ± 10% (i.e., uncertainty of the
concentration equations to calculate ground level concentration within a range of 10% from
the predicted value) for all the parameters in convective boundary layer (CBL) for surface
roughness length (Z
o
) value of 0.03 meter. When Z
o
is 1 meter, the uncertainty ranged
between 72 and 74%. In the case of stable boundary layer, the uncertainty ranged from 40 to
45% for the defined assumption cells. Bhat (2008) performed uncertainty and sensitivity
analyses for two Gaussian models used by Bower et al. (1979) and Chen et al. (1998) for
modeling bioaerosol emissions from land applications of class B biosolids. He observed
uncertainty ranges of 54 to 63% and 55 to 60% for Bowers et al. (1979) and Chen et al. (1998)
models respectively, for a ground level source.
Figures 1 through 6 present the uncertainty charts for both convective and stable
atmospheric conditions at different downwind distances. It was observed that the
atmospheric stability conditions influenced the uncertainty value. The uncertainty value
decreased as the atmospheric stability condition changed from convective to stable.

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Fig. 1. Uncertainty and Sensitivity Charts for 100 m Stack at 1000 m in CBL (Z
0

= 1 m).


Fig. 2. Uncertainty and Sensitivity Charts for 100 m Stack at 1000 m in CBL (Z
0
= 0.03 m).


Fig. 3. Uncertainty and Sensitivity Charts for 100 m stack at 10000 m in CBL (Z
0
= 1 m).



Fig. 4. Uncertainty and Sensitivity Charts for 100 m stack at 10000 m in CBL (Z
0
= 0.03 m).


Fig. 5. Uncertainty and Sensitivity Charts for 100 m stack at 1000 m in SBL.


Fig. 6. Uncertainty and Sensitivity Charts for 100 m stack at 10000 m in SBL.

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Estimation of uncertainty in predicting ground level concentrations from
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Fig. 1. Uncertainty and Sensitivity Charts for 100 m Stack at 1000 m in CBL (Z

0
= 1 m).


Fig. 2. Uncertainty and Sensitivity Charts for 100 m Stack at 1000 m in CBL (Z
0
= 0.03 m).


Fig. 3. Uncertainty and Sensitivity Charts for 100 m stack at 10000 m in CBL (Z
0
= 1 m).



Fig. 4. Uncertainty and Sensitivity Charts for 100 m stack at 10000 m in CBL (Z
0
= 0.03 m).


Fig. 5. Uncertainty and Sensitivity Charts for 100 m stack at 1000 m in SBL.


Fig. 6. Uncertainty and Sensitivity Charts for 100 m stack at 10000 m in SBL.

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The uncertainty analysis was also carried out for a 70 m and 40 m stack and the results
obtained are summarized below.

3.1.1b 70 m Stack
The predicted concentrations from a 70 m stack for the defined assumption cells have shown
an uncertainty range of 72 to 77% for an error of ± 10% for all the parameters in CBL for Z
o
=
0.03 m, and for the cases where Z
o
= 1 m, the uncertainty varied between 72 and 76%.i.e.
there is only 23 to 28% certainty that the predicted concentration will lie within the range of
10% from the actual concentration. In the case of SBL, an uncertainty range of 41 to 48% was
observed for the defined assumption cells concluding that the certainty of predicting
concentration is almost 52 to 59%.

3.1.1c 40 m Stack
The predicted concentrations from the 40 m stack for the defined assumption cells have
shown an uncertainty range of 70 to 77% and 70 to 76% for an error of ± 10% for all the
parameters in CBL for Z
o
= 0.03 m and Z
o
= 1 m respectively. In other words, the prediction
of concentration for 40 m stack is 27 to 30% times within the 10% range from observed
concentration. In the case of SBL, an uncertainty range of 41 to 47% was observed for the
defined assumptions cells.
From the above results it is clear that the prediction of concentration is less uncertain in
stable case as compared to the convective cases. The spreadsheet predict shows more
certainty in predicting concentrations in SBL as compared to that in CBL. Uncertainty ranges
for SBL and the case of CBL representing an urban area with large buildings were found to
be similar irrespective of the stack height considered. However, the uncertainty ranges

varied for the case of CBL representing an urban area with isolated buildings. The influence
of surface roughness is found to be more pronounced for a tall stack of 100 m where a much
wider range of uncertainty was observed as compared to 40 m and 70 m stack height cases.
The uncertainty in concentration results is not influenced by surface roughness for 70 m and
40 m stacks.

3.1.2 Uncertainty Analysis Summary
Table 8 provides a summary of the uncertainty ranges observed from the uncertainty charts
for the cases with the lowest and highest value of the parameters from the range of values
for the three days taken for analysis.












SBL CBL
Parameter
Low
Value

Uncertainty

Range

High
Value

Uncertainty

Range
Low
Value
Uncertainty

Range for
Zo = 1 m
Uncertainty

Range for
Zo = 0.03 m
High
Value

Uncertainty

Range for
Zo = 1 m
Uncertainty
Range for
Zo = 0.03 m
Wind
Speed
(ms
-1

)
1.5
38% to
40%
9.3
40% to
77%
3.6
73% to
76%
73% to
75%
8.2
71% to
76%
71% to
76%
Ambient
Temperature

(K)
263
34% to
37%
294.9

39% to
42%
267.5

72% to
76%
71% to
76%
302
54% to
63%
53% to
63%
Monin-
Obukhov
length (L)

38.4

38% to
40%
8888

40% to
77%
-8888

71% to
75%
71% to
76%
-356

67% to

77%
68% to
73%
Table 8. Summary of Uncertainty Ranges for Wind Speed, Ambient Temperature, and
Monin-Obukhov Length from the Three Stack Heights Considered.

One can observe the uncertainty ranges to be different for both CBL and SBL in Table 8.
Considering the case of wind speed, the averaged uncertainty value and range are observed
to be same for both the cases of wind speed being low and high irrespective of the surface
roughness length values in CBL. However, in the case of SBL, lower uncertainty range and
values are observed at low wind speed compared to high wind speed. On studying the case
of ambient temperature in SBL, less uncertainty was observed at lower ambient
temperatures as compared to higher ambient temperatures. In the case of a CBL, uncertainty
was observed to be more at lower ambient temperatures as compared to the uncertainty
observed at higher ambient temperatures irrespective of the surface roughness length
considered. Looking into the case of Monin-Obukhov length for stable atmosphere
conditions, one can observe less uncertainty and lower uncertainty range for lower value of
Monin-Obukhov length as compared to higher value of Monin-Obukhov length. In the case
of a CBL, lower values of Monin-Obukhov length produced higher uncertainty as compared
to higher Monin-Obukhov length values irrespective of surface roughness length.
Considering the case of low value of the parameters in SBL, one can observe similar
uncertainty ranges for wind speed and Monin-Obukhov length that is higher than the
uncertainty range observed in the case of ambient temperature. Similar trend can be
observed in the case of parameters with high value in SBL from Table 8. In the case of a CBL,
lower value for all the three parameters considered have shown similar uncertainty ranges
irrespective of surface roughness length. However, the uncertainty ranges for the cases of
higher value in CBL varied with each parameter. An ascending order of uncertainty range
and value in order of ambient temperature, Monin-Obukhov length, and wind speed can be
observed from Table 8 irrespective of surface roughness length values considered. One can
also observe the uncertainty values and ranges to be similar at any given low or high value

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Estimation of uncertainty in predicting ground level concentrations from
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The uncertainty analysis was also carried out for a 70 m and 40 m stack and the results
obtained are summarized below.

3.1.1b 70 m Stack
The predicted concentrations from a 70 m stack for the defined assumption cells have shown
an uncertainty range of 72 to 77% for an error of ± 10% for all the parameters in CBL for Z
o
=
0.03 m, and for the cases where Z
o
= 1 m, the uncertainty varied between 72 and 76%.i.e.
there is only 23 to 28% certainty that the predicted concentration will lie within the range of
10% from the actual concentration. In the case of SBL, an uncertainty range of 41 to 48% was
observed for the defined assumption cells concluding that the certainty of predicting
concentration is almost 52 to 59%.

3.1.1c 40 m Stack
The predicted concentrations from the 40 m stack for the defined assumption cells have
shown an uncertainty range of 70 to 77% and 70 to 76% for an error of ± 10% for all the
parameters in CBL for Z
o
= 0.03 m and Z
o
= 1 m respectively. In other words, the prediction
of concentration for 40 m stack is 27 to 30% times within the 10% range from observed
concentration. In the case of SBL, an uncertainty range of 41 to 47% was observed for the

defined assumptions cells.
From the above results it is clear that the prediction of concentration is less uncertain in
stable case as compared to the convective cases. The spreadsheet predict shows more
certainty in predicting concentrations in SBL as compared to that in CBL. Uncertainty ranges
for SBL and the case of CBL representing an urban area with large buildings were found to
be similar irrespective of the stack height considered. However, the uncertainty ranges
varied for the case of CBL representing an urban area with isolated buildings. The influence
of surface roughness is found to be more pronounced for a tall stack of 100 m where a much
wider range of uncertainty was observed as compared to 40 m and 70 m stack height cases.
The uncertainty in concentration results is not influenced by surface roughness for 70 m and
40 m stacks.

3.1.2 Uncertainty Analysis Summary
Table 8 provides a summary of the uncertainty ranges observed from the uncertainty charts
for the cases with the lowest and highest value of the parameters from the range of values
for the three days taken for analysis.












SBL CBL
Parameter

Low
Value

Uncertainty

Range
High
Value

Uncertainty

Range
Low
Value
Uncertainty

Range for
Zo = 1 m
Uncertainty

Range for
Zo = 0.03 m
High
Value

Uncertainty

Range for
Zo = 1 m
Uncertainty

Range for
Zo = 0.03 m
Wind
Speed
(ms
-1
)
1.5
38% to
40%
9.3
40% to
77%
3.6
73% to
76%
73% to
75%
8.2
71% to
76%
71% to
76%
Ambient
Temperature

(K)
263
34% to
37%

294.9

39% to
42%
267.5

72% to
76%
71% to
76%
302
54% to
63%
53% to
63%
Monin-
Obukhov
length (L)

38.4

38% to
40%
8888

40% to
77%
-8888

71% to

75%
71% to
76%
-356

67% to
77%
68% to
73%
Table 8. Summary of Uncertainty Ranges for Wind Speed, Ambient Temperature, and
Monin-Obukhov Length from the Three Stack Heights Considered.

One can observe the uncertainty ranges to be different for both CBL and SBL in Table 8.
Considering the case of wind speed, the averaged uncertainty value and range are observed
to be same for both the cases of wind speed being low and high irrespective of the surface
roughness length values in CBL. However, in the case of SBL, lower uncertainty range and
values are observed at low wind speed compared to high wind speed. On studying the case
of ambient temperature in SBL, less uncertainty was observed at lower ambient
temperatures as compared to higher ambient temperatures. In the case of a CBL, uncertainty
was observed to be more at lower ambient temperatures as compared to the uncertainty
observed at higher ambient temperatures irrespective of the surface roughness length
considered. Looking into the case of Monin-Obukhov length for stable atmosphere
conditions, one can observe less uncertainty and lower uncertainty range for lower value of
Monin-Obukhov length as compared to higher value of Monin-Obukhov length. In the case
of a CBL, lower values of Monin-Obukhov length produced higher uncertainty as compared
to higher Monin-Obukhov length values irrespective of surface roughness length.
Considering the case of low value of the parameters in SBL, one can observe similar
uncertainty ranges for wind speed and Monin-Obukhov length that is higher than the
uncertainty range observed in the case of ambient temperature. Similar trend can be
observed in the case of parameters with high value in SBL from Table 8. In the case of a CBL,

lower value for all the three parameters considered have shown similar uncertainty ranges
irrespective of surface roughness length. However, the uncertainty ranges for the cases of
higher value in CBL varied with each parameter. An ascending order of uncertainty range
and value in order of ambient temperature, Monin-Obukhov length, and wind speed can be
observed from Table 8 irrespective of surface roughness length values considered. One can
also observe the uncertainty values and ranges to be similar at any given low or high value
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of wind speed, ambient temperature, and Monin-Obukhov length in CBL irrespective of the
surface roughness length,
Hence, it can be inferred that the output of the AERMOD model is sensitive to the changes
in ambient temperature and Monin-Obukhov length for convective cases. However, one
needs to provide accurate wind speed, ambient temperature, and Monin-Obukhov length
rather than estimating the parameters so that uncertainty in the result is decreased.

Height of Stack (m) U (ms
-1
) L (m) T
a
(
o
K) Uncertainty
40
3.1
366.6
274.9 47%
287.5
44%
401.3

274.9
44%
287.5 48%
5.1
1821.5
265.9
46%
273.8
44%
1838.3
265.9 70%
273.8 72%
70
3.1
366.6
274.9
46%
287.5 42%
401.3
274.9 48%
287.5
43%
5.1
1821.5
265.9
50%
273.8 50%
1838.3
265.9
70%

273.8 74%
100
3.1
366.6
274.9
34%
287.5
39%
401.3
274.9
38%
287.5
42%
5.1
1821.5
265.9
54%
273.8
51%
1838.3
265.9
76%
273.8
72%
Table 9. Uncertainty Values for Different Heights of Stack at Point of Maximum Ground
Level Concentration in Stable Boundary Layer (SBL).

Table 10 presents the uncertainty obtained for different cases of parameters in a CBL. There
are two uncertainty values for each combination of parameters considered that represent
different surface roughness lengths considered. It can be observed from Table 10 that

uncertainty ranges were found to be similar for both surface roughness length cases, and
there is not much difference in the uncertainty value for any combination of the parameters
considered. For 40 m and 100 m stacks, one can observe the uncertainty to decrease with an
increase in wind speed regardless of increase or decrease in the values of other parameters
for both surface roughness lengths considered. However, similar trend could not be
observed in a 70 m stack and mixed results were observed. This concludes that stack height
is also a factor that can be responsible for sensitivity of the concentration prediction. There is

need to calculate the uncertainty in calculations due to stack height variation. It can also be
seen from Table 10 that irrespective of the ambient temperature, uncertainty observed for a
combination of lower values of wind speed and Monin-Obukhov length is more compared
to uncertainty observed for a combination of higher values of wind speed and Monin-
Obukhov length. Hence, one can infer the uncertainty to be more at lower parameter values
than higher parameter values for CBL conditions.

Height of stack (m) U (ms
-1
) L (m) T
a
(
o
K)
Uncertainty
Z
o
= 0.03 m Z
o
= 1 m
40
4.1

-2423.7
267.5 73% 70%
295.9 73% 75%
-356
267.5 75% 72%
295.9 73% 68%
6.7
-3345.8
268.1 68% 68%
302 65% 60%
-957.2
268.1 58% 63%
302 54% 53%
70
4.1
-2423.7
267.5 73% 73%
295.9 70% 68%
-356
267.5 70% 68%
295.9 70% 69%
6.7
-3345.8
268.1 75% 72%
302 68% 63%
-957.2
268.1 72% 76%
302 63% 75%
100
4.1

-2423.7
267.5 76% 70%
295.9 75% 74%
-356
267.5 63% 62%
295.9 54% 59%
6.7
-3345.8
268.1 68% 70%
302 60% 70%
-957.2
268.1 63% 58%
302 53% 54%
Table 10. Uncertainty Values for Different Heights of Stack at Point of Maximum Ground
Level Concentration in Convective Boundary Layer (CBL).

Irrespective of the stack heights considered, one can infer the uncertainty to be more at
higher wind speed, Monin-Obukhov length, and ambient temperature for stable boundary
conditions. An opposite trend is observed for CBL conditions, i.e., uncertainty was observed
to be more at lower wind speed, Monin-Obukhov length, and ambient temperature. One
can observe


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Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 189

of wind speed, ambient temperature, and Monin-Obukhov length in CBL irrespective of the
surface roughness length,
Hence, it can be inferred that the output of the AERMOD model is sensitive to the changes

in ambient temperature and Monin-Obukhov length for convective cases. However, one
needs to provide accurate wind speed, ambient temperature, and Monin-Obukhov length
rather than estimating the parameters so that uncertainty in the result is decreased.

Height of Stack (m) U (ms
-1
) L (m) T
a
(
o
K) Uncertainty
40
3.1
366.6
274.9 47%
287.5 44%
401.3
274.9 44%
287.5 48%
5.1
1821.5
265.9 46%
273.8 44%
1838.3
265.9 70%
273.8 72%
70
3.1
366.6
274.9 46%

287.5 42%
401.3
274.9 48%
287.5 43%
5.1
1821.5
265.9 50%
273.8 50%
1838.3
265.9 70%
273.8 74%
100
3.1
366.6
274.9 34%
287.5 39%
401.3
274.9 38%
287.5 42%
5.1
1821.5
265.9 54%
273.8 51%
1838.3
265.9 76%
273.8 72%
Table 9. Uncertainty Values for Different Heights of Stack at Point of Maximum Ground
Level Concentration in Stable Boundary Layer (SBL).

Table 10 presents the uncertainty obtained for different cases of parameters in a CBL. There

are two uncertainty values for each combination of parameters considered that represent
different surface roughness lengths considered. It can be observed from Table 10 that
uncertainty ranges were found to be similar for both surface roughness length cases, and
there is not much difference in the uncertainty value for any combination of the parameters
considered. For 40 m and 100 m stacks, one can observe the uncertainty to decrease with an
increase in wind speed regardless of increase or decrease in the values of other parameters
for both surface roughness lengths considered. However, similar trend could not be
observed in a 70 m stack and mixed results were observed. This concludes that stack height
is also a factor that can be responsible for sensitivity of the concentration prediction. There is

need to calculate the uncertainty in calculations due to stack height variation. It can also be
seen from Table 10 that irrespective of the ambient temperature, uncertainty observed for a
combination of lower values of wind speed and Monin-Obukhov length is more compared
to uncertainty observed for a combination of higher values of wind speed and Monin-
Obukhov length. Hence, one can infer the uncertainty to be more at lower parameter values
than higher parameter values for CBL conditions.

Height of stack (m) U (ms
-1
) L (m) T
a
(
o
K)
Uncertainty
Z
o
= 0.03 m Z
o
= 1 m

40
4.1
-2423.7
267.5
73%
70%
295.9
73%
75%
-356
267.5 75% 72%
295.9
73%
68%
6.7
-3345.8
268.1
68%
68%
302 65% 60%
-957.2
268.1 58% 63%
302
54%
53%
70
4.1
-2423.7
267.5 73% 73%
295.9 70% 68%

-356
267.5
70%
68%
295.9
70%
69%
6.7
-3345.8
268.1
75%
72%
302
68%
63%
-957.2
268.1
72%
76%
302
63%
75%
100
4.1
-2423.7
267.5
76%
70%
295.9
75%

74%
-356
267.5
63%
62%
295.9
54%
59%
6.7
-3345.8
268.1
68%
70%
302 60% 70%
-957.2
268.1 63% 58%
302
53%
54%
Table 10. Uncertainty Values for Different Heights of Stack at Point of Maximum Ground
Level Concentration in Convective Boundary Layer (CBL).

Irrespective of the stack heights considered, one can infer the uncertainty to be more at
higher wind speed, Monin-Obukhov length, and ambient temperature for stable boundary
conditions. An opposite trend is observed for CBL conditions, i.e., uncertainty was observed
to be more at lower wind speed, Monin-Obukhov length, and ambient temperature. One
can observe


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Air Quality190

3.2 Sensitivity Analysis
Sensitivity analysis determines the response of the AERMOD model to change in the values
of internal parameters. This helps us to determine how precisely and accurately the ground
level concentration (a particular parameter) could be calculated. The analysis is done using
the sensitivity charts that provide the percentage contribution to variance by the parameters
considered to the output of the AERMOD model. The parameters that have been considered
to perform sensitivity analysis are emission rate, stack exit velocity, stack temperature, wind
speed, lateral dispersion parameter, vertical dispersion parameter, weighting coefficients for
both updraft and downdraft, total horizontal distribution function, cloud cover, ambient
temperature, and surface roughness length. The contributions to variance by various
parameters considered at different downwind distances are tabulated in Table 11. The
parameters that contributed to variance are vertical dispersion parameter, horizontal
distribution (lateral dispersion parameter), emission rate, wind speed and weighting
coefficients. It should be noted that all the parameters considered for the sensitivity analysis
and that have zero contribution to the variance are not tabulated in Table 11. From the
sensitivity charts shown in Figures 1 to 6, one can observe wind speed to be having a
negative value for contribution to variance indicating that it is oppositely correlated, i.e.,
wind speed has an inverse effect on concentration. All other parameters had a positive
contribution to variance. The sensitivity analysis charts for predicted concentrations show
that vertical dispersion parameter and total horizontal distribution function have the
maximum influence to variance.

Condition Parameter
Contribution to variance in
CBL (%)
Contribution to
variance in SBL (%)
Z

o
= 1 m Z
o
= 0.03 m
1000
m
10000
m
1000
m
10000
m
1000 m 10000 m
100 meter stack
σ
z
67.5 53.2 85.4 87.5 22.4 10.8
F
y
25.9 45.1 11.5 10 64.5 76.1
Q 2.1 0.3 0.8 0.6 4 4.5
u -3 -1.1 -1.9 -1.3 -9 -8.6
λ
1
- 0.3 - - - -
λ
2
1.5 - 0.5 0.6 - -
70 meter stack
σ

z
84.4 86.4 84.9 86.4 33.3 14.9
F
y
12.1 10.5 11.7 10.4 53.9 68
Q 1.2 1 1.3 1.3 5.6 7.6
u -1.7 -1.6 -1.6 -1.4 -7.2 -9.5
λ
1
0.6 0.4 0.5 0.4 - -

40 meter stack
σ
z
82.1 85.9 81.9 85.7 28.4 15.9
F
y
13.6 11.1 14.1 11.1 58.2 66.2
Q 1.6 1.1 1.6 1.2 6.3 6.7
u -2.1 -1.4 -2 -1.6 -7.1 -11.2
λ
1
- 0.5 - 0.5 - -
λ
2
0.6 - 0.4 - - -
Low wind speed
σ
z
85.9 89.2 86 89.2 0 0.1

F
y
11.7 8.7 11.4 9.1 84.1 83.9
Q 0.7 0.4 0.8 0.5 4.6 5.1
u -1.1 -1.4 -1.3 -0.8 -11.3 -10.8
λ
1
0.5 0.3 0.5 0.3 - -
High wind speed
σ
z
84.3 89.4 83.3 89.4 5.2 4.7
F
y
13.8 8.7 13.4 8.4 78.8 79.7
Q 1 0.5 0.8 0.6 1.2 4.7
u -0.4 -1.1 -2 -1.2 -2.5 -10.8
λ
1
0.4 0.3 0.5 0.3 - -
Low ambient
temperature
σ
z
84.3 88.8 84.2 88.9 0.1 1.2
F
y
12.4 8.9 12.6 8.9 84.2 82.9
Q 0.8 0.6 0.8 0.7 5 4.9
u -1.9 -1.3 -1.9 -1.2 -10.7 -11

λ
1
0.6 0.3 0.5 0.4 - -
High ambient
temperature
σ
z
49.2 70.9 49.5 71.5 34.4 1.2
F
y
41.6 23.5 40.4 23.2 55.7 83.1
Q 2.3 1.4 2.7 1.5 3.2 4.9
u -5.5 -3.3 -5.7 -3 -6.6 -10.9
λ
1
1.5 0.9 1.6 0.9 - -
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Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 191

3.2 Sensitivity Analysis
Sensitivity analysis determines the response of the AERMOD model to change in the values
of internal parameters. This helps us to determine how precisely and accurately the ground
level concentration (a particular parameter) could be calculated. The analysis is done using
the sensitivity charts that provide the percentage contribution to variance by the parameters
considered to the output of the AERMOD model. The parameters that have been considered
to perform sensitivity analysis are emission rate, stack exit velocity, stack temperature, wind
speed, lateral dispersion parameter, vertical dispersion parameter, weighting coefficients for
both updraft and downdraft, total horizontal distribution function, cloud cover, ambient
temperature, and surface roughness length. The contributions to variance by various

parameters considered at different downwind distances are tabulated in Table 11. The
parameters that contributed to variance are vertical dispersion parameter, horizontal
distribution (lateral dispersion parameter), emission rate, wind speed and weighting
coefficients. It should be noted that all the parameters considered for the sensitivity analysis
and that have zero contribution to the variance are not tabulated in Table 11. From the
sensitivity charts shown in Figures 1 to 6, one can observe wind speed to be having a
negative value for contribution to variance indicating that it is oppositely correlated, i.e.,
wind speed has an inverse effect on concentration. All other parameters had a positive
contribution to variance. The sensitivity analysis charts for predicted concentrations show
that vertical dispersion parameter and total horizontal distribution function have the
maximum influence to variance.

Condition Parameter
Contribution to variance in
CBL (%)
Contribution to
variance in SBL (%)
Z
o
= 1 m Z
o
= 0.03 m
1000
m
10000
m
1000
m
10000
m

1000 m 10000 m
100 meter stack
σ
z
67.5 53.2 85.4 87.5 22.4 10.8
F
y
25.9 45.1 11.5 10 64.5 76.1
Q 2.1 0.3 0.8 0.6 4 4.5
u -3 -1.1 -1.9 -1.3 -9 -8.6
λ
1
- 0.3 - - - -
λ
2
1.5 - 0.5 0.6 - -
70 meter stack
σ
z
84.4 86.4 84.9 86.4 33.3 14.9
F
y
12.1 10.5 11.7 10.4 53.9 68
Q 1.2 1 1.3 1.3 5.6 7.6
u -1.7 -1.6 -1.6 -1.4 -7.2 -9.5
λ
1
0.6 0.4 0.5 0.4 - -

40 meter stack

σ
z
82.1 85.9 81.9 85.7 28.4 15.9
F
y
13.6 11.1 14.1 11.1 58.2 66.2
Q 1.6 1.1 1.6 1.2 6.3 6.7
u -2.1 -1.4 -2 -1.6 -7.1 -11.2
λ
1
- 0.5 - 0.5 - -
λ
2
0.6 - 0.4 - - -
Low wind speed
σ
z
85.9 89.2 86 89.2 0 0.1
F
y
11.7 8.7 11.4 9.1 84.1 83.9
Q 0.7 0.4 0.8 0.5 4.6 5.1
u -1.1 -1.4 -1.3 -0.8 -11.3 -10.8
λ
1
0.5 0.3 0.5 0.3 - -
High wind speed
σ
z
84.3 89.4 83.3 89.4 5.2 4.7

F
y
13.8 8.7 13.4 8.4 78.8 79.7
Q 1 0.5 0.8 0.6 1.2 4.7
u -0.4 -1.1 -2 -1.2 -2.5 -10.8
λ
1
0.4 0.3 0.5 0.3 - -
Low ambient
temperature
σ
z
84.3 88.8 84.2 88.9 0.1 1.2
F
y
12.4 8.9 12.6 8.9 84.2 82.9
Q 0.8 0.6 0.8 0.7 5 4.9
u -1.9 -1.3 -1.9 -1.2 -10.7 -11
λ
1
0.6 0.3 0.5 0.4 - -
High ambient
temperature
σ
z
49.2 70.9 49.5 71.5 34.4 1.2
F
y
41.6 23.5 40.4 23.2 55.7 83.1
Q 2.3 1.4 2.7 1.5 3.2 4.9

u -5.5 -3.3 -5.7 -3 -6.6 -10.9
λ
1
1.5 0.9 1.6 0.9 - -
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Air Quality192

Low Monin-
Obukhov length
σ
z
83.7 89.1 83.6 89.0 0 0.1
F
y
13.1 8.9 13.2 8.7 84.1 83.9
Q 0.9 0.4 0.9 0.5 4.6 5.1
u -1.7 -1.2 -1.8 -1.3 -11.3 -10.8
λ
1
0.5 0.4 0.5 0.4 - -
High Monin-
Obukhov length
σ
z
76.9 84.3 77.5 87.5 5.2 4.7
F
y
18.8 9.4 18.1 9.7 78.8 79.7
Q 1 0.6 1.0 0.7 1.2 4.7
U -2.7 -5.3 -2.6 -1.5 -2.5 -10.8

λ
1
0.6 0.4 0.8 0.5 - -
Table 11. Contribution to Variance by Parameters in Calculation of Concentration at
Different Downwind Distances.

The contributions to variance of parameters in both CBL and SBL for 1000 m and 10000 m
downwind distance are tabulated in Table 11. In CBL, contribution to variance by vertical
dispersion parameter is more than the contribution from horizontal distribution function
which is a function of lateral dispersion parameter, indicating pollutant concentration to be
more sensitive to vertical dispersion parameter than lateral dispersion parameter. However,
it is the opposite in SBL, i.e., pollutant concentration is more sensitive to lateral dispersion
parameter than vertical dispersion parameter. Wind speed parameter had a negative
contribution to variance irrespective of the boundary layer conditions at both downwind
distances. The contribution to variance by weighting coefficients is found to be negligible in
all the conditions.
For the condition considering stack heights from Table 11, the pollutant concentration
sensitiveness increased with downwind distance for vertical dispersion parameter and wind
speed, but decreased for the remaining parameters in CBL for both surface roughness
lengths considered. In SBL, contribution to variance by vertical dispersion parameter
reduced with increase in downwind distance and increased for all other parameters
considered for analysis.
For the condition considering low and high wind speeds from Table 11, in CBL, the
pollutant concentration sensitiveness increased with downwind distance for vertical
dispersion parameter. Pollutant concentration sensitiveness varied with surface roughness.
For the case of Z
0
being 1 m pollutant concentration sensitiveness decreased with increase in
downwind distance and the opposite trend is observed for the case of Z
0

being 0.03 m. For
all other parameters pollutant concentration sensitiveness decreased with increase in
downwind distance. In SBL, pollutant concentration sensitiveness decreased for vertical
dispersion parameter as downwind distance increased and one can note that for lower wind
speed, the contribution to variance by vertical dispersion parameter is zero at both 1000 m
and 10000 m.

For the condition of ambient temperature in CBL, the contribution of variance by vertical
dispersion parameter and wind speed increased with downwind distance and decreased for
all other parameters for both the surface roughness lengths considered. Similar pattern can
be observed in SBL for the condition of lower ambient temperature with the exception that
wind speed showed an opposite trend to that observed in CBL. However, for the case of
higher ambient temperature, in SBL, the contribution to variance increases for horizontal
distribution and emission rate, and decreases for vertical dispersion parameter and wind
speed with increase in downwind distance. For both high and low values of ambient
temperature, the contribution by wind speed was significant in SBL compared to CBL. Thus,
one can state that the concentrations are more sensitive to higher temperatures and wind
speed in SBL than in CBL.
The sensitiveness in Monin-Obukhov length condition showed similar behavior to that of
wind speed condition. It was observed that emission rate had more contribution to variance
than vertical dispersion parameter in SBL for the cases having lower values of Monin-
Obukhov length, wind speed, and ambient temperature. The remaining parameters defined
in the assumption cells have negligible contribution to variance when compared to vertical
dispersion parameter and total horizontal distribution function.

4. Conclusions
The objective of the study was to perform uncertainty and sensitivity analyses in predicting
the concentrations from the AERMOD equations. As it is difficult to perform uncertainty
and sensitivity analyses using the original AERMOD model, an approximate set of
AERMOD equations were programmed in Excel. The predicted concentrations from the

AERMODCBL and AERMODSBL models were compared to the predicted concentrations
from AERMOD model. The comparison has shown that the predicted concentration values
from the spreadsheet ranged between 87% and 107%, as compared to the predicted
concentration values from the AERMOD model. This showed that the predicted
concentrations obtained by the modeled equations can be relied upon to perform
uncertainty and sensitivity analyses for both atmospheric conditions.
Uncertainty and sensitivity analysis has been performed for different cases taken into
consideration by varying stack height, wind speed, Monin-Obukhov length, and ambient
temperature for three days and source data as summarized in Tables 3, 4, and 5. The
conclusions made from the study are listed below.
1. A user-friendly tool [60], that can calculate downwind contaminant concentrations
under different boundary layer conditions has been developed using the AERMOD
equations.
2. The uncertainty range varies between 67% and 75% for convective conditions on
averaging the uncertainty values from all the considered cases, while in stable
conditions, it ranged from 40% to 47%. This means the predictions are less certain
in convective cases.
3. The contribution to variance by vertical dispersion parameter (σ
z
) is found to be
82% under convective conditions i.e. the predicted concentrations are highly
influenced by σ
z.
. In the case of horizontal distribution (F
y
), the contribution to
variance was found to be 75% in the stable case.
www.intechopen.com
Estimation of uncertainty in predicting ground level concentrations from
direct source releases in an urban area using the USEPA’s AERMOD model equations 193

Low Monin-
Obukhov length
σ
z
83.7 89.1 83.6 89.0 0 0.1
F
y
13.1 8.9 13.2 8.7 84.1 83.9
Q 0.9 0.4 0.9 0.5 4.6 5.1
u -1.7 -1.2 -1.8 -1.3 -11.3 -10.8
λ
1
0.5 0.4 0.5 0.4 - -
High Monin-
Obukhov length
σ
z
76.9 84.3 77.5 87.5 5.2 4.7
F
y
18.8 9.4 18.1 9.7 78.8 79.7
Q 1 0.6 1.0 0.7 1.2 4.7
U -2.7 -5.3 -2.6 -1.5 -2.5 -10.8
λ
1
0.6 0.4 0.8 0.5 - -
Table 11. Contribution to Variance by Parameters in Calculation of Concentration at
Different Downwind Distances.

The contributions to variance of parameters in both CBL and SBL for 1000 m and 10000 m
downwind distance are tabulated in Table 11. In CBL, contribution to variance by vertical
dispersion parameter is more than the contribution from horizontal distribution function
which is a function of lateral dispersion parameter, indicating pollutant concentration to be
more sensitive to vertical dispersion parameter than lateral dispersion parameter. However,
it is the opposite in SBL, i.e., pollutant concentration is more sensitive to lateral dispersion
parameter than vertical dispersion parameter. Wind speed parameter had a negative
contribution to variance irrespective of the boundary layer conditions at both downwind
distances. The contribution to variance by weighting coefficients is found to be negligible in
all the conditions.
For the condition considering stack heights from Table 11, the pollutant concentration
sensitiveness increased with downwind distance for vertical dispersion parameter and wind
speed, but decreased for the remaining parameters in CBL for both surface roughness
lengths considered. In SBL, contribution to variance by vertical dispersion parameter
reduced with increase in downwind distance and increased for all other parameters
considered for analysis.
For the condition considering low and high wind speeds from Table 11, in CBL, the
pollutant concentration sensitiveness increased with downwind distance for vertical
dispersion parameter. Pollutant concentration sensitiveness varied with surface roughness.
For the case of Z
0
being 1 m pollutant concentration sensitiveness decreased with increase in
downwind distance and the opposite trend is observed for the case of Z
0
being 0.03 m. For
all other parameters pollutant concentration sensitiveness decreased with increase in
downwind distance. In SBL, pollutant concentration sensitiveness decreased for vertical
dispersion parameter as downwind distance increased and one can note that for lower wind
speed, the contribution to variance by vertical dispersion parameter is zero at both 1000 m
and 10000 m.

For the condition of ambient temperature in CBL, the contribution of variance by vertical
dispersion parameter and wind speed increased with downwind distance and decreased for
all other parameters for both the surface roughness lengths considered. Similar pattern can
be observed in SBL for the condition of lower ambient temperature with the exception that
wind speed showed an opposite trend to that observed in CBL. However, for the case of
higher ambient temperature, in SBL, the contribution to variance increases for horizontal
distribution and emission rate, and decreases for vertical dispersion parameter and wind
speed with increase in downwind distance. For both high and low values of ambient
temperature, the contribution by wind speed was significant in SBL compared to CBL. Thus,
one can state that the concentrations are more sensitive to higher temperatures and wind
speed in SBL than in CBL.
The sensitiveness in Monin-Obukhov length condition showed similar behavior to that of
wind speed condition. It was observed that emission rate had more contribution to variance
than vertical dispersion parameter in SBL for the cases having lower values of Monin-
Obukhov length, wind speed, and ambient temperature. The remaining parameters defined
in the assumption cells have negligible contribution to variance when compared to vertical
dispersion parameter and total horizontal distribution function.

4. Conclusions
The objective of the study was to perform uncertainty and sensitivity analyses in predicting
the concentrations from the AERMOD equations. As it is difficult to perform uncertainty
and sensitivity analyses using the original AERMOD model, an approximate set of
AERMOD equations were programmed in Excel. The predicted concentrations from the
AERMODCBL and AERMODSBL models were compared to the predicted concentrations
from AERMOD model. The comparison has shown that the predicted concentration values
from the spreadsheet ranged between 87% and 107%, as compared to the predicted
concentration values from the AERMOD model. This showed that the predicted
concentrations obtained by the modeled equations can be relied upon to perform
uncertainty and sensitivity analyses for both atmospheric conditions.

Uncertainty and sensitivity analysis has been performed for different cases taken into
consideration by varying stack height, wind speed, Monin-Obukhov length, and ambient
temperature for three days and source data as summarized in Tables 3, 4, and 5. The
conclusions made from the study are listed below.
1. A user-friendly tool [60], that can calculate downwind contaminant concentrations
under different boundary layer conditions has been developed using the AERMOD
equations.
2. The uncertainty range varies between 67% and 75% for convective conditions on
averaging the uncertainty values from all the considered cases, while in stable
conditions, it ranged from 40% to 47%. This means the predictions are less certain
in convective cases.
3. The contribution to variance by vertical dispersion parameter (σ
z
) is found to be
82% under convective conditions i.e. the predicted concentrations are highly
influenced by σ
z.
. In the case of horizontal distribution (F
y
), the contribution to
variance was found to be 75% in the stable case.
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